Quantum Simulation of the Two-Dimensional Weyl Equation in a Magnetic Field

TL;DR

This paper demonstrates the quantum simulation of a 2D Weyl particle in a magnetic field using trapped ions, revealing key relativistic phenomena like Landau levels and spin dynamics, thus extending quantum simulation capabilities in particle physics.

Contribution

It introduces a method to simulate 2D relativistic particles with magnetic fields in ion traps, capturing complex spin and spatial dynamics not previously explored.

Findings

Observation of linear dispersion relation

Detection of discrete Landau levels

Verification of helicity conservation

Abstract

Quantum simulation of 1D relativistic quantum mechanics has been achieved in well-controlled systems like trapped ions, but properties like spin dynamics and response to external magnetic fields that appear only in higher dimensions remain unexplored. Here we simulate the dynamics of a 2D Weyl particle. We show the linear dispersion relation of the free particle and the discrete Landau levels in a magnetic field, and we explicitly measure the spatial and spin dynamics from which the conservation of helicity and properties of antiparticles can be verified. Our work extends the application of an ion trap quantum simulator in particle physics with the additional spatial and spin degrees of freedom.